Question

Help Me!! Limit Definition. :( Problem attached :)

Answer 1

i believe they mean:

\[f'(x) = \lim_{h -> 0} \frac{ f(x+h) - f(x) }{ h }\]

Answer 2

that's it? then whats the difference between that and the difference quotient??

Answer 3

@Euler271 am i finding the derivative of the difference quotient?

Answer 4

No, the derivative is the limit of the difference quotient.

Answer 5

@John_ES so do i solve it normally and take the derivative?

Answer 6

To calculate the derivative with the definition you calculate the difference quotient, and then, the limit.

Answer 7

The result will be the derivative.

Answer 8

@John_ES oh thats confusing

Answer 9

\[\frac{ (t-7t^2-3)-(t-7t^2) }{ 3}\] is this what i do?

Answer 10

It must be something like this,
\[\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\rightarrow 0}\frac{x+h-7(x+h)^2-(x-7x^2)}{h}\]

Answer 11

Where I put x there must be a t, sorry.

Answer 12

You cannot substitute h.

Answer 13

with the number 3, I mean.

Answer 14

You can use the other definition of a derivative,
\[f'(a)=\lim_{t\rightarrow a}\frac{f(t)-f(a)}{t-a}\]

Answer 15

In this one you can substitute a with 3.

Answer 16

yea but i have to do the limit definition for this one... where did u get t=h-7(t+h)^2 i don't understand that part

Answer 17

the = should be a +

Answer 18

When you do,
\[f(t+h)\]in
\[f(t)=t-7t^2\]You must substitute t with t+h,
\[f(t+h)=t+h-7(t+h)^2\]

Answer 19

Can you solve the problem from this point?

Answer 20

yea thanks

Answer 21

;)